AN INTEGRAL REPRESENTATION OF MULTIPLE HURWITZ–LERCH ZETA FUNCTIONS AND GENERALIZED MULTIPLE BERNOULLI NUMBERS
AN INTEGRAL REPRESENTATION OF MULTIPLE HURWITZ–LERCH ZETA FUNCTIONS AND GENERALIZED MULTIPLE BERNOULLI NUMBERS
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多重HURWITZ-LERCH ZETA函数和广义多重伯努利数的积分表示
DOI：
10.1093/qmath/hap004
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发表时间：
2010
影响因子：
0.7
通讯作者：
Y. Komori
中科院分区：
文献类型：
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作者：
Y. Komori
给出了Hurwitz-Lerch Zeta函数多重推广的曲面积分表示，它直接类似于著名的Hankel型Riemann Zeta函数的轮廓积分表示.从这个积分表示出发，我们得到了它可能的奇点集合的详细描述。此外，我们还利用Bernoulli数的推广给出了非正整数上Zeta函数的特殊值的两个公式。这些结果是对以前已知结果的改进。
A surface integral representation of a multiple generalization of the Hurwitz–Lerch zeta function is given, which is a direct analogue of the well-known contour integral representation of the Riemann zeta function of Hankel's type. From this integral representation, we derive a detailed description of the set of its possible singularities. In addition, we present two formulae for special values of the zeta function at non-positive integers in terms of generalizations of Bernoulli numbers. These results are refinements of previously known ones.